The Dynamics of Somite Patterns in Embryos
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- 英文论文题名：The Dynamics of Somite Patterns in Embryos
- 论文作者：关利南 ; 申建伟
- 英文论文作者：Guan Linan ; Shen Jianwei ; School of Mathematics and Statistics ; Zhengzhou University ; School of Mathematics and Statistics ; Xuchang University
- 年：2016
- 作者机构：School of Mathematics and Statistics, Zhengzhou University;School of Mathematics and Statistics, Xuchang University;
- 英文论文关键词：Hopf bifurcation ; bistable ; somitogenesis
- 会议召开时间：2016-08-04
- 会议录名称：第三届全国神经动力学学术会议论文摘要集
- 语种：英文
- 分类号：Q132
- 学会代码：AGLU
- 会议名称：第三届全国神经动力学学术会议
- 会议地点：中国甘肃敦煌
- 主办单位：中国力学学会动力学与控制专业委员会神经动力学专业组
- 学会名称：中国力学学会
- 页数：1
- 文件大小：610k
- 原文格式：D
- 会议级别：全国
摘要
Using a systematic computational approach and in vivo experiments, Cotterell et al.challenge a 40-year-old model that explains large-scale embryonic patterns in terms of long-range gradients. Instead, they show that these patterns can arise from short-range interactions and that a modified reaction diffusion mechanism can drive the self-organization observed during somitogenesis.In this paper, we inves-tigated the modified two dimensional model. It is suitable for exploring a design space of somitogenesis and can explain aspects of somitogenesis that previous models cannot. We mainly studied the non-diffusing case.We have used the Hopf bifurcation theorem,bifurcation theory and the Center manifold theorem in our investigation. Our model exhibits subcritical Hopf bifurcation for certain parameter values which marks the instability of limit cycles destroyed in Hopf bifurcations. And we get the condition in which the bistable state of the system exists. Because somitogenesis in the process of biological development occupies an important position,and as a pattern process can be used to study pattern formation and many aspects of embryogenesis. So our study have a great help for Embryonic development,gene expression,cell differen-tiation.In addition to,it is beneficial to study the clone animal variation problem of spinal bone number.
Using a systematic computational approach and in vivo experiments, Cotterell et al.challenge a 40-year-old model that explains large-scale embryonic patterns in terms of long-range gradients. Instead, they show that these patterns can arise from short-range interactions and that a modified reaction diffusion mechanism can drive the self-organization observed during somitogenesis.In this paper, we inves-tigated the modified two dimensional model. It is suitable for exploring a design space of somitogenesis and can explain aspects of somitogenesis that previous models cannot. We mainly studied the non-diffusing case.We have used the Hopf bifurcation theorem,bifurcation theory and the Center manifold theorem in our investigation. Our model exhibits subcritical Hopf bifurcation for certain parameter values which marks the instability of limit cycles destroyed in Hopf bifurcations. And we get the condition in which the bistable state of the system exists. Because somitogenesis in the process of biological development occupies an important position,and as a pattern process can be used to study pattern formation and many aspects of embryogenesis. So our study have a great help for Embryonic development,gene expression,cell differen-tiation.In addition to,it is beneficial to study the clone animal variation problem of spinal bone number.
Using a systematic computational approach and in vivo experiments, Cotterell et al.challenge a 40-year-old model that explains large-scale embryonic patterns in terms of long-range gradients. Instead, they show that these patterns can arise from short-range interactions and that a modified reaction diffusion mechanism can drive the self-organization observed during somitogenesis.In this paper, we inves-tigated the modified two dimensional model. It is suitable for exploring a design space of somitogenesis and can explain aspects of somitogenesis that previous models cannot. We mainly studied the non-diffusing case.We have used the Hopf bifurcation theorem,bifurcation theory and the Center manifold theorem in our investigation. Our model exhibits subcritical Hopf bifurcation for certain parameter values which marks the instability of limit cycles destroyed in Hopf bifurcations. And we get the condition in which the bistable state of the system exists. Because somitogenesis in the process of biological development occupies an important position,and as a pattern process can be used to study pattern formation and many aspects of embryogenesis. So our study have a great help for Embryonic development,gene expression,cell differen-tiation.In addition to,it is beneficial to study the clone animal variation problem of spinal bone number.
引文
[1]Kulesa,P.M.,Schnell,S.,Rudloff,S.,Baker,R.E.,and Maini,P.K.,From segment to somite:segmentation to epithelialization analyzed within quantitative frameworks.Dev.Dyn.236(2007)1392–1402.
[2]Cotterell,J.,Robert-Moreno,A.,and Sharpe,J.,A Local,Self-Organizing Reaction-Diffusion Model Can Explain Somite Patterning in Embryos.Cell Systems,1(4)(2015)257-269.
[3]Cooke,J.,and Zeeman,E.C.,A clock and wavefront model for control of the number of repeated structures during animal morphogenesis.J.Theor.Biol.58(1976)455–476.
[2]Cotterell,J.,Robert-Moreno,A.,and Sharpe,J.,A Local,Self-Organizing Reaction-Diffusion Model Can Explain Somite Patterning in Embryos.Cell Systems,1(4)(2015)257-269.
[3]Cooke,J.,and Zeeman,E.C.,A clock and wavefront model for control of the number of repeated structures during animal morphogenesis.J.Theor.Biol.58(1976)455–476.